@HS - They don't sound right as Standard English, but the first one, at least, is quite normal in dialect, and of course there's the famous 'The boy done good'. Dialects have different rules, and in some English dialects adjectives are commonly used as adverbs.

But Fowler is obviously writing in Standard English. I'm wondering if this use was perhaps commoner in the past, or if, on the other hand, I'm simply alone in finding it odd.

Ngram would seem to support the first theory, with 'comes natural' being quite popular between about 1880 and about 1940, with interestingly a peak in the late twenties (Fowler's book was published in 1926). 'Comes naturally' was always more common, but whereas the ratio (in British books) in 1880 was little more than 2:1, it is now more like 12:1.